WRITE ALGEBRAIC EXPRESSION FOR VERBAL EXPRESSION

The following table will help us to learn some of the words (phrases) that can be used to indicate mathematical operations :  Algebraic expression word problems examples with answers

In each case, write algebraic expression for the given verbal phrase.

Example 1 :

Sum of x and twice y.

Answer :

x + 2y

Example 2 :

Subtraction of z from y.

Answer :

y - z

Example 3 :

Twice the sum of m and n.

Answer :

2(m + n)

Example 4 :

b decreased by twice a.

Answer :

b - 2a

Example 5 :

Sum of the squares of x and y.

Answer :

x² + y²

Example 6 :

Two times the product of a and b divided by 5.

Answer :

2ab/5

Example 7 :

Product of p and q added to 7.

Answer :

pq + 7

Example 8 :

x more than two-third of y.

Answer :

x + (2/3)y

Example 9 :

Half of a number x decreased by 3.

Answer :

(x/2) - 3

Example 10 :

Sum of numbers m and n decreased by their product.

Answer :

(m + n) - mn

Example 11 :

4 times x less than sum of y and 6.

Answer :

(y + 6) - 4x

Example 12 :

Double the sum of one third of a and m.

Answer :

2[(1/3)a + m]

Example 13 :

18 is taken away from 8 times of a number.

Answer :

Let x be the number.

8x -18

Example 14 :

The denominator of a fraction exceeds the numerator by 5.

Answer :

Let x be the numerator.

x/(x + 5)

Example 15 :

If thrice of A's age 6 years ago be subtracted from twice his present age.

Answer :

Let x be the present age of A.

Then, A's age 6 years ago = x - 6.

2x - 3(x - 6)

Example 16 :

Five times a number increased by seven is equal to forty-seven. What is the number?

Answer :

Let x be the required number.

5x + 7 = 47

5x = 47 - 7

5x = 40

x = 40/5

x = 8

So, the required number is 8.

Work with a partner. After you have written the expression, evaluate it using mental math or some other method.

Example 16 :

You wash cars for 2 hours. You receive $6. How much do you earn per hour?

Answer :

Number of hours working = 2

Amount i have recieved = $6

Amount he earns per hour = 6/2

= 3

So, amount he earns per hour is $3.

Example 17 :

You have $60. You buy a pair of jeans and a shirt. The pair of jeans costs $27. You come home with $15. How much did you spend on the shirt?

Answer :

Cost of pair of jean = $27

Amount she has returned to home = 15

Amount you have initially = $60

Amount spent = 60-15

= 45

Amount spent = 45

Cost of pair of jean + cost of shirt = 45

27 + cost of shirt = 45

cost of shirt = 45 - 27

= 18

So, cost of shirt is $18.

Example 18 :

Suppose the man in the St. Ives poem has x wives, each wife has x sacks, each sack has x cats, and each cat has x kits. Write an expression using exponents that represents the total number of kits, cats, sacks, and wives going to St. Ives.

Answer :

For example, number of wives be 3, number of sacks be 2.

Number of sacks = 2 + 2 + 2 (or) 3(2) ==> 6

Number of wives = x

Number of sacks = x (x) = x2

Each sack has x cats

Number of cats = x (x) (x) ==> x³

Each cats has x kits

Number of kits = x(x)(x)(x) ==> x⁴

Example 19 :

The expression 20a + 13c is the cost (in dollars) for a adults and c students to enter a science center.

a. How much does it cost for an adult? a student? Explain your reasoning.

b. Find the total cost for 4 adults and 24 students.

Answer :

Given expressions is, 20 a + 13 c

a - number of adults and c - number of students.

a)

Cost for 1 adult ticket = 20

Cost of 1 student ticket = 13

b) 

Number of adults = 4, then a = 4

Number of students = 24, then c = 24

Required cost = 20 (4) + 13 (24)

= 80 + 312

= 392

Example 20 :

The length of Interstate 90 from the West Coast to the East Coast is 153.5 miles more than 2 times the length of Interstate 15 from southern California to northern Montana. Let m be the length of Interstate 15. Which expression can you use to represent the length of Interstate 90?

A)  2m + 153.5      B)  2m − 153.5

C)  153.5 − 2m      D) 153.5m + 2

Answer :

The word times means multiplication. So, multiply 2 and m

The correct answer is A) 2m + 153.5

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